What is difference between ATX PSU's and ATX12V ones?

ATX, introduced in late 1995, defined three types of power connectors:
1) 4-pin "Molex connector" transferred directly from AT standard
2) 4-pin Berg floppy connector — transferred directly from AT standard
3) 20-pin Molex Mini-fit Jr. main motherboard connector — new to the ATX standard.
A supplemental 6-pin AUX connector providing additional 3.3 V and 5 V supplies to the motherboard, if needed. This was used to power the CPU in motherboards with CPU voltage regulator modules which required 3.3 volt and/or 5 volt rails and could not get enough power through the regular 20-pin header.

Use of a 24-pin Main Power Connector over 20-pin Connector for PCI Express Support
6-Pin Aux Power Connector Not Required
Use of Dual 12V Rails if Greater than 20A
Serial ATA Power Connectors Required

ATX12V 1.x
While designing the Pentium 4 platform in 1999/2000, the standard 20-pin ATX power connector was found insufficient to meet increasing power-line requirements; the standard was significantly revised into ATX12V 1.0

ATX12V 1.0
The main changes and additions in ATX12V 1.0 (released in February 2000) were:
Increased the power on the 12 V rail (power on 5 V and 3.3 V rails remained mostly the same.
An extra 4-pin 12-volt connector to power the CPU. Referred to as the P4 connector because this was first needed to support the Pentium 4 processor.

ATX12V 2.0 (introduced in February 2003), up to the current version of the ATX12V spec, published in April 2013 - ATX12V v2.4

Since you provided no information concerning your hardware, I wouldn't know what you should get.

A great PSU and no caompatiblity issue. But man! Way overkill for 1080 Ti SLI. An 850W unit is enough for that, even with OC'ing. And I gotta say, price must not be an issue for you. $3600+ is a chunk of change ;)
Sep 24, 2018

OK. I plan on adding a "few" extra parts, and I don't want to take any chances, even if all I need is 850W unit. The build the link leads to is a basic build. My real build has a few other things, and the real one is still a maybe. Also my other question, because I'm also helping a friend pick out parts. What kind of things would affect whether you get a ATX PSU or a ATX12V PSU. That's the last thing I'm still confused on...

Years ago, the ATX protocol called for a 20-pin connector for the motherboard. That changed over time to a 20+4 pin or 24-pin connector. A few other changes were made as well, mostly in the available voltages at the connector. The PSU name changed along with it to ATX12V. But today, the name ATX and ATX12V are used interchangeably. Any new PSU you find for your system today will be an ATX12V no matter what they refer to it as.
You can get a quick brush-up on the subject here.